Partial classification of Lorenz knots: Syllable permutations of torus knots words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.

Potenciar a consciência fonológica de crianças pré-escolares em contexto naturalístico

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ciências da Educação Especialidade Intervenção Precoce

Letter names and sounds: their implications for the phonetisation process

Our aim was to analyse the impact of the characteristics of words used in spelling programmes and the nature of instructional guidelines on the evolution from grapho-perceptive writing to phonetic writing in preschool children. The participants were 50 5-year-old children, divided in five equivalent groups in intelligence, phonological skills and spelling. All the children knew the vowels and the consonants B, D, P, R, T, V, F, M and C, but didn’t use them on spelling. Their spelling was evaluated in a pre and post-test with 36 words beginning with the consonants known. In-between they underwent a writing programme designed to lead them to use the letters P and T to represent the initial phonemes of words. The groups differed on the kind of words used on training (words whose initial syllable matches the name of the initial letter—Exp. G1 and Exp. G2—versus words whose initial syllable is similar to the sound of the initial letter—Exp. G3 and Exp. G4). They also differed on the instruction used in order to lead them to think about the relations between the initial phoneme of words and the initial consonant (instructions designed to make the children think about letter names—Exp. G1 and Exp. G3 —versus instructions designed to make the children think about letter sounds—Exp. G2 and Exp. G4). The 5th was a control group. All the children evolved to syllabic phonetisations spellings. There are no differences between groups at the number of total phonetisations but we found some differences between groups at the quality of the phonetisations.